Bifurcations of traveling wave solutions for the magma equation |
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| Authors: | Yixiang Geng Lixiang Zhang |
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| Institution: | a Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming, Yunnan 650051, China
b Faculty of Environmental Science and Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China |
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| Abstract: | The traveling wave solutions of the magma equation are studied by using the approach of dynamical systems and the theory of bifurcations. With the aid of Maple, all bifurcations and phase portraits in the parametric space are obtained. Under different regions of parametric space, various sufficient conditions to guarantee the existence of solitary wave, periodic wave and breaking wave solutions are given. Moreover, the reason for appearance of breaking waves is explained. |
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| Keywords: | Solitary wave solution Periodic wave solution Breaking wave solution Theory of bifurcation Magma equation |
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